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Volume 34, Issue 3
On the Solution Accuracy Downstream of Shocks When Using Godunov-Type Schemes. I. Sources of Errors in One-Dimensional Problems

Alexander V. Rodionov

DOI: 10.4208/cicp.OA-2022-0243

Commun. Comput. Phys., 34 (2023), pp. 749-786.

Published online: 2023-10

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  • Abstract

The article opens a series of publications devoted to a systematic study of numerical errors behind the shock wave when using high-order Godunov-type schemes, including in combination with the artificial viscosity approach. The proposed paper describes the numerical methods used in the study, and identifies the main factors affecting the accuracy of the solution for the case of one-dimensional gas dynamic problems. The physical interpretation of the identified factors is given and their influence on the grid convergence is analyzed.

  • Keywords

Shock-capturing methods, Riemann problem, WENO reconstruction, Runge-Kutta method, Hancock-Rodionov method, artificial viscosity approach, Shu-Osher test problem.

  • AMS Subject Headings

65M08, 65M12, 35L65, 35L67

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-34-749, author = {Rodionov , Alexander V.}, title = {On the Solution Accuracy Downstream of Shocks When Using Godunov-Type Schemes. I. Sources of Errors in One-Dimensional Problems}, journal = {Communications in Computational Physics}, year = {2023}, volume = {34}, number = {3}, pages = {749--786}, abstract = {

The article opens a series of publications devoted to a systematic study of numerical errors behind the shock wave when using high-order Godunov-type schemes, including in combination with the artificial viscosity approach. The proposed paper describes the numerical methods used in the study, and identifies the main factors affecting the accuracy of the solution for the case of one-dimensional gas dynamic problems. The physical interpretation of the identified factors is given and their influence on the grid convergence is analyzed.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0243}, url = {http://global-sci.org/intro/article_detail/cicp/22023.html} }
TY - JOUR T1 - On the Solution Accuracy Downstream of Shocks When Using Godunov-Type Schemes. I. Sources of Errors in One-Dimensional Problems AU - Rodionov , Alexander V. JO - Communications in Computational Physics VL - 3 SP - 749 EP - 786 PY - 2023 DA - 2023/10 SN - 34 DO - http://doi.org/10.4208/cicp.OA-2022-0243 UR - https://global-sci.org/intro/article_detail/cicp/22023.html KW - Shock-capturing methods, Riemann problem, WENO reconstruction, Runge-Kutta method, Hancock-Rodionov method, artificial viscosity approach, Shu-Osher test problem. AB -

The article opens a series of publications devoted to a systematic study of numerical errors behind the shock wave when using high-order Godunov-type schemes, including in combination with the artificial viscosity approach. The proposed paper describes the numerical methods used in the study, and identifies the main factors affecting the accuracy of the solution for the case of one-dimensional gas dynamic problems. The physical interpretation of the identified factors is given and their influence on the grid convergence is analyzed.

Alexander V. Rodionov. (2023). On the Solution Accuracy Downstream of Shocks When Using Godunov-Type Schemes. I. Sources of Errors in One-Dimensional Problems. Communications in Computational Physics. 34 (3). 749-786. doi:10.4208/cicp.OA-2022-0243
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